In large bowl, whisk together the flour, baking soda, and salt. Set aside.<
Let’s brown some butter: In medium-low heat, melt the butter. Rise the heat to medium and cook until the butter gently boils. Cook until the butter starts to brown and it develops a dark color. Carefully pour the browned butter into a bowl to cool for ten minutes.

In the bowl of your stand mixer, cream butter and sugar until pale and fluffy using the paddle attachment (you could also beat it with a hand mixer). Beat in the eggs one by one, waiting until each has been incorporated to add the next. Beat in vanilla extract and mashed bananas. Add half of the flour mixture to the butter mix and beat on low speed. Scrape down the sides of the bowl to incorporate. Add in the buttermilk and beat until incorporated followed by the remaining flour mixture; scrape the sides of the bowl to incorporate.

Bake for 45-50 minutes, or until a toothpick inserted into the center of the cake comes out clean and the top springs back when lightly pressed.
Allow cake to cool for 10 minutes in the pan, then turn cake out onto a wire rack to cool completely.